Power distribution networks transmit three phase power from a power generation plant to power stations over transmission lines. The three phases are of equal frequency and magnitude, but are offset by one third of the phase. The sum of the currents is zero and a transmission line for one phase can therefore act as the return path for the lines of the other two phases. When loads on the phases are equal, this represents a balanced condition, which is ideal for efficiency. Variation from the balanced condition reduces efficiency. At power stations, transformers step down transmission line voltages. Feeder medium voltage lines carry voltage to a final transformer that reduces voltage to load usage levels, e.g. 120V and 240V. The connections of customers are made to distributed loads on the three phases. Modern power distribution networks include complex systems for managing distribution of the power. Complex tools help to visualize and predict network conditions, and act as a support system to personnel to take control steps. However, mere visualization and simulation tools provide little help in terms of analysis or improvement of distribution, due to the complexity of the distribution systems. Power distribution networks face growing and highly variable (low to high and high to low) load demands. At installation, loads are usually balanced across a three-phase distribution system. Unbalance arises from growth of the load demand as well as changes in load demand during time period. Balanced feeders can drift over time to unbalance. Instabilities and unbalances can produce substantial power losses in a network and can cause power outages.
Static or dynamic corrections are traditionally used to stabilize networks. The corrections provide voltage regulation to maintain voltage within an allowable tolerance of a desired constant value. Networks also include capacitor banks that counteract power factor lag and phase shifts.
Phase swapping is a direct technique that seeks to balance a system at each load point of a feeder system. Various researchers have explored phase swapping approaches for load balancing. In practice, phase adjustments are made manually according to a calculated phase vector. Manual adjustments are conducted infrequently, such as once a year during equipment maintenance or service. Load conditions can vary greatly during the interval between manual adjustments, causing the network to depart from the calculated phase vector, leading to higher power losses.
One heuristic search algorithm for calculating vectors to perform such manual adjustments considered measured constant and changing load. This algorithm and manual adjustment approach was tested within the service area of the Taipei South District. Y.-Y. Hsu, J.-H. Yi, S. S. Liu, Y. Chen, H. C. Feng, and Y. M. Lee, “Transformer and feeder load balancing using a heuristic search approach,” Power Systems, IEEE Transactions on, vol. 8, pp. 184-190, February 1993. A positive impact was observed.
Additional efforts have been made to accurately characterize a power distribution network to improve performance between manual adjustments. Various example approaches are discussed in the following paragraphs.
A mixed integer programming formulation for phase swapping has been considered. J. Zhu, M.-Y. Chow, and F. Zhang, “Phase balancing using mixed-integer programming [distribution feeders],” Power Systems, IEEE Transactions on, vol. 13, pp. 1487-1492, November 1998. Single-phase loads are treated differently than three-phase loads. Nodal phase swapping and lateral phase swapping are discussed in that paper.
Simulated Annealing (SA) is another heuristic algorithm. J. Zhu, G. Bilbro, and M.-Y. Chow, “Phase balancing using simulated annealing,” Power Systems, IEEE Transactions on, vol. 14, pp. 1508-1513, November 1999. This technique formulates the phase balancing problem as Mixed-Integer Programming (MIP) approach and provides a global solution calculation.
Another heuristic approach rephases single- and double-phase laterals in to circuit loss while also maintaining/improving imbalances at various balance point locations. M. Dilek, R. Broadwater, J. Thompson, and R. Seqiun, “Simultaneous phase balancing at substations and switches with time-varying load patterns,” Power Systems, IEEE Transactions on, vol. 16, pp. 922-928, November 2001. The algorithm allows a limit on the number of phase move operations and exclusion of certain laterals.
A multi-objective fuzzy self-adaptive particle swarm optimization evolutionary algorithm considering fuel cell power plants in the distribution network has been proposed. T. Niknam, H. Meymand, H. Mojarrad, and J. Aghaei, “Multi-objective daily operation management of distribution network considering fuel cell power plants,” Renewable Power Generation, IET, vol. 5, no. 5, pp. 356-367, 2011.
A distributed control algorithm that can regulate the power output of multiple photovoltaic generators (PVs) has also proposed. H. Xin, Z. Qu, J. Seuss, and A. Maknouninejad, “A self-organizing strategy for power flow control of photovoltaic generators in a distribution network,” Power Systems, IEEE Transactions on, vol. 26, no. 3, pp. 1462-1473, 2011.
Many researches have proposed models to accurately characterize systems. These models are helpful to understand systems and unbalance issues that can arise. See, e.g. T.-H. Chen, M.-S. Chen, T. Inoue, P. Kotas, and E. Chebli, “Three-phase cogenerator and transformer models for distribution system analysis,” Power Delivery, IEEE Transactions on, vol. 6, no. 4, pp. 1671-1681, 1991.
Unbalance remains a practical problem despite significant efforts to better characterize networks and provide strategies to initially set and later make manual adjustments. Efforts to maintain balance are conducted during maintenance or when a new load is added. Periodically, work crews rebalance feeders during periods of maintenance or restoration, when a new customer is to be connected, or if the percentage of unbalance exceeds some number and the phase balance for existing feeders has become significantly unbalanced. Three factors are normally considered in making a decision to re-balance a feeder: the monetary cost of making the tap change(s), the expected increase in feeder balance and the temporary interruption of power to the customer. Current phase rebalance is complicated and typically conducted manually at sufficient expense. Legacy power meters that remain in widespread operation lack the ability to communicate, be programmed or adjusted except for by costly manual service.